arXiv subjects

Amit Sharma

Publications and source records attributed to Amit Sharma.

At least 19 recordsLinked to original sources

arXiv2026

On modules whose pure submodules are essential in direct summands

We introduce the notion of \emph{pure extending modules}, a refinement of classical extending modules in which only pure submodules are required to be essential in direct summands. Fundamental properties and characterizations are established, showing that pure extending and extending modules coincide over von Neumann regular rings. As an application, we prove that pure extending modules admit decomposition patterns analogous to those in the classical theory, including a generalization of the Osofsky--Smith theorem: a cyclic module whose proper factor modules are pure extending decomposes into a finite direct sum of pure-uniform submodules. We establish sufficient conditions under which central quasi-morphicity and central morphicity coincide, notably for finitely generated, nonsingular, pure extending modules over noetherian rings, and for modules over semisimple artinian rings.

math.RA↗

arXiv2026

Central quasi-morphicity, central morphicity, and strongly $π$-regularity

This paper revisits the notions of centrally morphic and centrally quasi-morphic modules introduced by Dehghani and Sedaghatjoo. We identify sufficient conditions under which these notions become equivalent. In particular, if a module $ M $ is image-projective, generates its kernels, and its endomorphism ring has von Neumann regular center, then central morphicity, central quasi-morphicity, and right central morphicity of the endomorphism ring are equivalent. We also prove that centrally morphic rings with von Neumann regular center and ACC on principal right annihilators are strongly $π$-regular.

math.RA↗

arXiv2026

Accurate Trace Estimation with Fewer Random Bits via Recursive TensorSketch

We consider the problem of estimating the trace of an implicit matrix $\mathbf{A} \in \mathbb{R}^{d^p\times d^p}$ that can only be accessed through matrix-vector products queries. The \textit{Hutchinson trace estimator}% ~\cite{Girard1987algorithme, article-hutchinson} is a classical sketching method for this problem. Their estimator, $H_{m}(\mathbf{A}) = \frac{1}{m} \sum_{i=1}^{m} {\mathbf{z}^{(i)}}^T \mathbf{A} \mathbf{z}^{(i)}, \quad \text{where } \ {\mathbf{z}^{(i)}}\in \mathbb{R}^{d^p}$, and $z^{(i)}_j \in {N}(0, 1), j\in [d^p]$, satisfies the following guarantees: (i) $\mathbb{E}[H_{m}(\mathbf{A})]=\operatorname{tr}(\mathbf{A})$, and (ii) $\mathrm{Var}[H_{m}(\mathbf{A})]=\frac{2}{m}||\mathbf{A}||_F^2$. Generating one query vector $\mathbf{z}^{(i)}$ requires $O(d^p)$ random bits; thus, $m$ queries require $O(md^p)$ random bits, which can be prohibitive in large-scale applications. Recent work by Meyer et al.~\cite{meyer2025hutchinsonsestimatorbadkroneckertraceestimation} proposes a variant of the Hutchinson trace estimator in which each query vector in $\mathbb{R}^{d^p}$ is constructed as the Kronecker product of $p$ random vectors in $\mathbb{R}^d$, requiring $O(mpd)$ random bits for $m$ query vectors. The estimator of~\cite{meyer2025hutchinsonsestimatorbadkroneckertraceestimation} is unbiased; however, its variance grows exponentially with $p$. In this work, we address this limitation by proposing a sketching-based estimator that requires $O\!\big(p (d + m)\log m\big)$ random bits, yields an unbiased estimate of the trace, and simultaneously achieves a variance bound that grows polynomially with $p$.

cs.LG↗

arXiv2026

When Agents Say One Thing and Do Another: Validating Elicited Beliefs from LLMs

Large language models (LLMs) are increasingly deployed in high-stakes settings where good decisions require forming beliefs over the probability of unknown outcomes. However, it is unclear whether LLMs act as if they hold coherent beliefs when making decisions, or if so, how we could validate models' reports of such beliefs. We propose a decision-theoretic framework that elicits both probability judgments and decisions from an agent and tests their mutual consistency. Formally, our methods characterize whether it is possible for the actions to be produced by a ``near-rational" decision maker who holds the elicited probability as their true belief. We show that, perhaps surprisingly, this formalization implies empirically testable conditions even without any assumption about the agent's utility function. Applying our framework to stylized clinical diagnosis tasks, we find that models' reported beliefs are demonstrably imperfect summaries of the information revealed in their decisions, but that the discrepancies are small for the strongest models.

cs.AI↗

arXiv2026

Rethinking LLM Verification: Evidence Structure, Uncertainty, and Selective Refinement

Large language models (LLMs) often rely on shortcuts rather than systematic reasoning, raising safety concerns in medical applications. Allowing models to abstain when uncertain improves reliability but introduces a coverage accuracy tradeoff. We propose a two-stage framework for medical hypothesis verification in multiple-choice settings that manages this tradeoff through targeted ontology grounding, applied only when the model abstains. We show that abstention is not random but reflects genuine uncertainty, with abstained predictions associated with lower confidence. Across two frontier models (GPT-5.5, accessed via the Azure OpenAI API, and DeepSeek-R1), the proposed framework improves question-level accuracy by 9.6 percentage points (82.9% to 92.5%) and hypothesis-level accuracy by 4.2 percentage points (92.0% to 96.2%). Our experiments conducted on MedReason and MedQA show that abstention can be repurposed as a control signal for selective reasoning refinement, achieving knowledge-graph-level performance without explicit knowledge graph construction.

cs.CV↗

arXiv2026

Improving TensorSketch Using Complex Random Variables

\texttt{TensorSketch} by~\cite{pham2013fast,kar2012random} provides efficient sketching algorithms for high-dimensional polynomial kernels $\vec{x}^{\otimes p} \in \R^{d^p}$. \cite{kar2012random} uses dense Johnson-Lindenstrauss (JL)-type projections with computational cost $O(pDd)$, where $D$ denotes the sketch dimension, whereas~\cite{pham2013fast} extends the sparse \texttt{CountSketch}~\citep{count_sketch} algorithm, yielding a faster algorithm for high-dimensional sparse inputs with running time $O\big(p(\nnz{\vec{x}} + D \log D)\big)$. However, the variance of both estimators grows exponentially with the polynomial degree $p$, scaling as $3^{p}/D$. Recent work by~\cite{pmlr-v206-wacker23a} showed that using complex-valued distribution reduces this dependence to $2^{p}/D$ for the approach of~\cite{kar2012random}. However, their method relies on dense JL-type projections with computational cost $O(pDd)$ and does not extend to the algorithm of~\cite{pham2013fast}. In this work, we introduce a simple variant of \texttt{TensorSketch}~\citep{pham2013fast} that achieves the same variance bound as~\cite{pmlr-v206-wacker23a}, while retaining its advantage of the input-sparsity running time. We validate our results with supporting experiments on synthetic and real-world datasets.

cs.DS↗

arXiv2026

VERDICT: Training-Free Step-Wise Verification of Multimodal Reasoning via Disagreement-Aware Consensus

Multimodal large language models often generate reasoning chains containing subtle errors that lead to incorrect answers. Current verification approaches have notable limitations. Existing approaches either require expensive labelled supervision with inconsistent cross-task performance or aggregate scores from multiple sources by simple aggregations, missing a key insight: when these scores disagree, that disagreement itself carries important information about whether a reasoning step is truly valid or not. We formalise this as a coupled scoring problem among disparate, frozen verifiers, interpretable as a coordination game with a unique closed-form equilibrium where agreement signals valid steps while disagreement reveals instability. Towards this end, we propose a training-free domain-agnostic step-wise verification approach we call VERDICT: VERification via Disagreement-Informed Coupled Thresholding. To our knowledge, VERDICT is the first training-free verifier that makes the structure of cross-modal disagreement explicit and actionable. It computes consensus scores through a closed-form solution, enabling both disagreement-aware filtering and stability-conscious ranking of reasoning steps. Evaluated across six benchmarks, \method consistently improves over the base model by up to +5.95%, and performs competitively with domain-specific critics that demand extensive supervision, demonstrating that cross-modal agreement provides robust verification signals without task-specific adaptation and Training-Free Verification

cs.AI↗

arXiv2026

FedChronos: Federated Fine-Tuning of Time-Series Foundation Models for Privacy-Preserving Commodity Price Forecasting

Time-series foundation models (TSFMs) such as Chronos have demonstrated strong forecasting capabilities across domains, yet adapting them to institutionally fragmented settings, where data cannot be centralized due to regulatory, competitive, or sovereignty constraints, remains unexplored. We introduce FedChronos, a framework for federated parameter-efficient fine-tuning of an already pre-trained TSFM, a setting that existing federated time-series work has not addressed, since prior methods either pre-train from scratch or align prototypes rather than adapt a fixed backbone. Our approach applies Low-Rank Adaptation (LoRA) to the Chronos-T5 backbone and trains across distributed clients using FedAvg and FedProx, transmitting only lightweight adapter weights (384~KB per round, an 86$\times$ reduction over full-model exchange). We evaluate FedChronos on daily commodity prices from 15 Indian agricultural markets across 9 states, a naturally non-IID federated setting, and find that naïve LoRA fine-tuning overfits substantially on small per-client datasets, dropping below zero-shot performance. We further observe that differential privacy (DP) noise can act as implicit regularization and counteract this overfitting: in our experiments the strongest configuration ($\varepsilon = 5$) reduces mean absolute percentage error (MAPE) by 31% over zero-shot and 26% over the best traditional baseline, while bounding each round's information leakage via per-round $(\varepsilon, δ)$-differential privacy. Because the model is compact and the updates are small, the approach also suits edge AI deployments where both the network link and the client device are constrained. Overall, our findings suggest that privacy and accuracy can be complementary rather than competing objectives in federated TSFM fine-tuning.

cs.LG↗

arXiv2026

MeDxAgent: Multi-Agent Consultation for Interactive Medical Diagnosis

Large language models (LLMs) are increasingly used for health-related decision support. Yet most evaluations treat diagnosis as a single-shot task with complete information provided upfront, often as a multiple-choice selection. This diverges from clinical practice, where diagnosis is interactive and open-ended, involving sequential hypothesis refinement through targeted questioning. We address this gap. We build MeDxBench, a large-scale benchmark of 4,421 clinical cases across 20 specialties. We further propose MeDxAgent, a multi-agent consultation system for interactive diagnosis, and systematically study its prompt-, flow- and agent-level design choices. MeDxAgent achieves a 10.3% accuracy gain over the baseline on MeDxBench, closing 52.3% of the gap to a full-information oracle. We find that specific design choices: collecting demographics first, passing summarized dialogue for diagnosis, and feeding candidate diagnoses for targeted questioning, improve accuracy, mirroring how physicians reason, though their effect emerges fully only in combination. Code and dataset will be released upon publication.

cs.MA↗

arXiv2026

A Nash Equilibrium Framework For Training-Free Multimodal Step Verification

Multimodal large language models often generate reasoning chains containing subtle errors that lead to incorrect answers. Current verification approaches have notable limitations. Learned critics need extensive labeled data and show inconsistent performance across different tasks. Meanwhile, existing training-free methods simply average scores from different sources, missing a key insight: when these scores disagree, that disagreement itself carries important information about whether a reasoning step is truly valid or not. We propose a training-free verification approach that treats step-wise verification as a coordination problem among specialized judges. We formalize these judges' interaction as a Nash equilibrium game where agreement signals valid steps while disagreement reveals instability. Our method computes equilibrium scores through a closed-form solution, enabling both disagreement-aware filtering and stability-conscious ranking of reasoning steps. Evaluated across six benchmarks, our approach achieves consistent improvements of 2.4% to 5.2% over baseline models and shows competitive performance against learned critics, demonstrating that cross-modal agreement (not just average confidence) provides robust verification signals without task-specific adaptation.

cs.CV↗

arXiv2026

interwhen: A Generalizable Framework for Steering Reasoning Models with Test-time Verification

Reasoning models produce long traces of intermediate decisions and tool calls, making test-time verification important for ensuring correctness. Existing approaches either verify only the final answer, which misses early errors, or rely on branch-and-verify strategies that explore multiple trajectories. We introduce interwhen, a single-trajectory verification framework that steers model behavior by providing feedback on intermediate reasoning traces. It addresses two key challenges. First, given a set of verifiers, obtaining verifiable states from the reasoning trace typically requires prompt engineering or external task decomposition into fixed steps. Instead, we propose a monitoring system that periodically polls the reasoning trace and forks inference of the reasoning model to recover intermediate states. Verifiers are run asynchronously alongside generation, adding negligible overhead on correct executions and intervening only when violations occur. Second, beyond math and code, a central challenge for process verification is the scarcity of verifiers. interwhen addresses this through automatic verifier synthesis from natural-language policy documents. Given a policy, it can generate code-based verifiers, including provably correct verifiers in Lean and z3. Together, these contributions yield a plug-and-play test-time verification system that can improve task completion and policy compliance of any reasoning agent. On reasoning benchmarks where policies encode mathematical or logical constraints, interwhen achieves near-perfect accuracy for reasoning models using a fraction of the tokens of baselines. On agentic benchmarks with policy-based verifier generation, it enables improvements in task quality for SLMs without any finetuning, e.g., task completion rate of Qwen3-30B jumps from 32% to 87% on the telecom domain in tau2-bench. Code at https://github.com/microsoft/interwhen.

cs.LO↗

arXiv2026

HORIZON: A Benchmark for In-the-wild User Behaviour Modeling

User behavior in the real world is diverse, cross-domain, and spans long time horizons. Existing user modeling benchmarks however remain narrow, focusing mainly on short sessions and next-item prediction within a single domain. Such limitations hinder progress toward robust and generalizable user models. We present HORIZON, a new benchmark that reformulates user modeling along three axes i.e. dataset, task, and evaluation. Built from a large-scale, cross-domain reformulation of Amazon Reviews, HORIZON covers 54M users and 35M items, enabling both pretraining and realistic evaluation of models in heterogeneous environments. Unlike prior benchmarks, it challenges models to generalize across domains, users, and time, moving beyond standard missing-positive prediction in the same domain. We propose new tasks and evaluation setups that better reflect real-world deployment scenarios. These include temporal generalization, sequence-length variation, and modeling unseen users, with metrics designed to assess general user behavior understanding rather than isolated next-item prediction. We benchmark popular sequential recommendation architectures alongside LLM-based baselines that leverage long-term interaction histories. Our results highlight the gap between current methods and the demands of real-world user modeling, while establishing HORIZON as a foundation for research on temporally robust, cross-domain, and general-purpose user models.

cs.IR↗

arXiv2026

Improving Generative Methods for Causal Evaluation via Simulation-Based Inference

Generating synthetic datasets that accurately reflect real-world observational data is critical for evaluating causal estimators, but it remains a challenging task. Existing generative methods offer a solution by producing synthetic datasets anchored in the observed data (source data) while allowing variation in key parameters such as the treatment effect and amount of confounding bias. However, it is often unclear which generative methods to use and which values of parameters to choose when generating synthetic datasets. Moreover, existing methods typically require users to provide fixed point estimates of such parameters. This denies users the ability to express uncertainty over both generative methods and parameter values and removes the potential for posterior inference, potentially leading to unreliable estimator comparisons. We introduce simulation-based inference for causal evaluation (SBICE), a framework that treats the generative method and its corresponding generative parameters as uncertain and infers their posterior distribution given a source dataset. Leveraging techniques in simulation-based inference, SBICE identifies suitable generative methods and infers distributions over its parameter configurations to produce synthetic datasets closely aligned with the source data distribution. Empirical results demonstrate that SBICE improves the reliability of estimator evaluations by generating realistic datasets whose causal estimates closely match the estimates of the source data, making it a robust and uncertainty-aware approach to selecting causal estimators.

cs.LG↗

arXiv2026

FrugalRAG: Less is More in RL Finetuning for Multi-Hop Question Answering

Reinforcement learning (RL) based on the final answer's reward has driven recent progress in small language models (SLMs) on reasoning-heavy tasks such as math and code. However, applying the same techniques to retrieval-augmented generation (RAG) benchmarks like multi-hop QA has yielded limited gains, often trailing supervised or prompting-only baselines. Instead, we argue that a viable path for RL in multi-hop QA is to use test-time scaling judiciously to optimize both final answer accuracy and efficiency in reaching that answer. We propose FrugalRAG, a two-stage finetuning framework that adaptively reduces the number of retrieval steps based on a question's difficulty. First, we train an SLM with supervised finetuning on a full-exploration policy that generates broad sub-queries. Then, we apply RL to adaptively prune search depth based on question difficulty, directly rewarding policies that balance correctness with frugality. Unlike prior approaches requiring 10x more data, our method achieves competitive performance with only approximately 1,000 examples. On HotPotQA and other multi-hop QA benchmarks, FrugalRAG attains state-of-the-art efficiency-accuracy tradeoffs, cutting retrieval cost nearly in half. Moreover, on the challenging BrowseCompPlus benchmark, it generalizes zero-shot and surpasses SLM-based and other baselines. These results demonstrate the use of RL not to increase reasoning steps, but to reduce them, as an effective solution for scalable and efficient RAG.

cs.CL↗

arXiv2026

Better Think Thrice: Learning to Reason Causally with Double Counterfactual Consistency

Despite their strong performance on reasoning benchmarks, large language models (LLMs) have proven brittle when presented with counterfactual questions, suggesting weaknesses in their causal reasoning ability. While recent work has demonstrated that labeled counterfactual tasks can be useful benchmarks of LLMs' causal reasoning, producing such data at the scale required to cover the vast potential space of counterfactuals is limited. In this work, we introduce double counterfactual consistency (DCC), a lightweight inference-time method for measuring and guiding the ability of LLMs to reason causally. Without requiring labeled counterfactual data, DCC verifies a model's ability to execute two important elements of causal reasoning: causal intervention and counterfactual prediction. Using DCC, we evaluate the causal reasoning abilities of various leading LLMs across a range of reasoning tasks and interventions. Moreover, we demonstrate the effectiveness of DCC as a training-free test-time rejection sampling criterion and show that it can directly improve performance on reasoning tasks across multiple model families.

cs.LG↗

arXiv2025

Teaching Transformers Causal Reasoning through Axiomatic Training

For text-based AI systems to interact in the real world, causal reasoning is an essential skill. Since active interventions are costly, we study to what extent a system can learn causal reasoning from symbolic demonstrations of causal axioms. Specifically, we present an axiomatic training method where the system learns from multiple demonstrations of a causal axiom (or rule), rather than incorporating the axiom as an inductive bias or inferring it from data values. A key question is whether the system would learn to generalize from the axiom demonstrations to more complex scenarios. Our results, based on applying axiomatic training to learn the transitivity axiom and d-separation rule, indicate that such generalization is possible. To avoid data contamination issues, we start with a 67 million parameter transformer model and train it from scratch. On both tasks, we find that a model trained on linear causal chains (along with some noisy variations) can generalize well to complex graphs, including longer causal chains, causal chains with reversed order, and graphs with branching.To handle diverse text inputs, the same method is extended to finetune language models. Finetuning Llama-3-8B-Instruct model on our axiomatic data leads to significant gains on causal benchmarks such as Corr2Cause and CLEAR, in some cases providing state-of-the-art performance surpassing GPT-4.

cs.LG↗

arXiv2025

Realizing LLMs' Causal Potential Requires Science-Grounded, Novel Benchmarks

Recent claims of strong performance by Large Language Models (LLMs) on causal discovery are undermined by a key flaw: many evaluations rely on benchmarks likely included in pretraining corpora. Thus, apparent success suggests that LLM-only methods, which ignore observational data, outperform classical statistical approaches. We challenge this narrative by asking: Do LLMs truly reason about causal structure, and how can we measure it without memorization concerns? Can they be trusted for real-world scientific discovery? We argue that realizing LLMs' potential for causal analysis requires two shifts: (P.1) developing robust evaluation protocols based on recent scientific studies to guard against dataset leakage, and (P.2) designing hybrid methods that combine LLM-derived knowledge with data-driven statistics. To address P.1, we encourage evaluating discovery methods on novel, real-world scientific studies. We outline a practical recipe for extracting causal graphs from recent publications released after an LLM's training cutoff, ensuring relevance and preventing memorization while capturing both established and novel relations. Compared to benchmarks like BNLearn, where LLMs achieve near-perfect accuracy, they perform far worse on our curated graphs, underscoring the need for statistical grounding. Supporting P.2, we show that using LLM predictions as priors for the classical PC algorithm significantly improves accuracy over both LLM-only and purely statistical methods. We call on the community to adopt science-grounded, leakage-resistant benchmarks and invest in hybrid causal discovery methods suited to real-world inquiry.

cs.LG↗

arXiv2025

Executable Counterfactuals: Improving LLMs' Causal Reasoning Through Code

Counterfactual reasoning, a hallmark of intelligence, consists of three steps: inferring latent variables from observations (abduction), constructing alternatives (interventions), and predicting their outcomes (prediction). This skill is essential for advancing LLMs' causal understanding and expanding their applications in high-stakes domains such as scientific research. However, existing efforts in assessing LLM's counterfactual reasoning capabilities tend to skip the abduction step, effectively reducing to interventional reasoning and leading to overestimation of LLM performance. To address this, we introduce executable counterfactuals, a novel framework that operationalizes causal reasoning through code and math problems. Our framework explicitly requires all three steps of counterfactual reasoning and enables scalable synthetic data creation with varying difficulty, creating a frontier for evaluating and improving LLM's reasoning. Our results reveal substantial drop in accuracy (25-40%) from interventional to counterfactual reasoning for SOTA models like o4-mini and Claude-4-Sonnet. To address this gap, we construct a training set comprising counterfactual code problems having if-else condition and test on out-of-domain code structures (e.g. having while-loop); we also test whether a model trained on code would generalize to counterfactual math word problems. While supervised finetuning on stronger models' reasoning traces improves in-domain performance of Qwen models, it leads to a decrease in accuracy on OOD tasks such as counterfactual math problems. In contrast, reinforcement learning induces the core cognitive behaviors and generalizes to new domains, yielding gains over the base model on both code (improvement of 1.5x-2x) and math problems. Analysis of the reasoning traces reinforces these findings and highlights the promise of RL for improving LLMs' counterfactual reasoning.

cs.LG↗